Well, yes, that's kinda the point. — Banno

What do you mean? You're the one who brought up ¬p → ¬◇Kp, not me. I am simply explaining that this is not true a priori because ¬p ⊬ □¬(p ∧ JBp).

Are you saying this is invalid? — Banno

No, I'm saying that ◇Kp ⊬ p, just as ◇p ⊬ p, and so ¬p ∧ ◇Kp is consistent, just as ¬p ∧ ◇p is consistent.

So both the antecedent and the consequent of your biconditional are false. This should be apparent after you performed the substitution:

¬p → ¬◇(p ∧ JBp) ↔︎ ◇(p ∧ JBp) → p

This is unsound because:

◇(p ∧ JBp) ⊬ p
¬p ⊬ □¬(p ∧ JBp)

The issue here is how to formulate antirealism so that it is constant with there being things we don't know. — Banno

That's been done. As the article says:

The intuitionistic anti-realist takes solace in the fact that she is not committed to the blatantly absurd claim that all truths are known.

...

Notice that T-knowability is free of the paradoxes that we have discussed. It is free of Fitch’s paradox and the related undecidedness paradox.

...

Dummett’s knowability principle or DKP, like Tennant’s, is not threatened by the knowability paradoxes, and for the same reason.

The antirealist claims that there are unknown truths but that all unknown truths of the appropriate kind¹ are knowable. With respect to ontology, there are unverified truths but there are no verification-transcendent truth conditions.

_{1 e.g. p exists and has property q}

you think realism inconsistent in all cases? — Banno

I'm not arguing against realism. I am explaining that you are misrepresenting anti-realism. It isn't what you think it is; it neither claims nor entails that all truths are known, it isn't idealism, and it isn't phenomenalism. That there are things we don't know and that things exist even when we don't see them doesn't refute anti-realism.

Or to phrase this differently, it is possible, logically speaking, that your are indeed a vat brain - Putnam's argument fails to show otherwise. — Banno

It certainly does attempt to, arguing that the correct theory of meaning entails that it is not logically possible that we are brains in a vat. But I'm not trying to argue about the merits of Putnam's argument against the possibility of brains in a vat; I'm simply explaining why the case is made that "it counts against realism that it might permit global skepticism".

If something is not true then it is not possible to know it is true; hence if it is possible to know something then it is true. — Banno

This is not how modal possibility works. Again, you confuse ¬p ∧ ◇Kp with ◇(¬p ∧ Kp).

◇Kp means ◇(p ∧ JBp), where JBp means that p is justifiably believed. ◇(p ∧ JBp) does not entail p and so ◇Kp does not entail p.

Again, I'm suggesting that the choice between applying realist and antirealist logics is context-dependent. So I do not agree that "every meaningful declarative sentence is either true or false" and hence I do not agree that counterfactuals must be either true or false. — Banno

So you're an anti-realist about counterfactuals?

No. Realism is applicable when "a, b, and c and so on exist, and the fact that they exist and have properties such as F-ness, G-ness, and H-ness is independent of anyone’s beliefs, linguistic practices, conceptual schemes, and so on", and to this list we can add knowledge. In cases where truth is dependent on anyone’s beliefs, linguistic practices, conceptual schemes, or knowledge, then antirealism might be applicable. — Banno

And now you're back to failing to distinguish between Kp and ◇Kp.

The antirealist allows for p ∧ ¬Kp, regardless of what Fitch might think. The anti-realist very explicitly says that there are things we don't know.

The relevant concern is whether or not something exists that is impossible to know exists. The anti-realist says that nothing like this exists. If something exists then it is possible to know that it exists (even if we don't in fact know). As Dummett says, there are no verification-transcendent truth conditions (which is not the same as saying that there are no unverified truths).

There is a relevance argument against BIV. You take Realism ⊨ ◇BIV, which i thinks is overreach. I say Realism → (BIV v ~BIV), and for independent reasons ~BIV. — Banno

Assuming the law of excluded middle, BIV ∨ ¬BIV is a truism, and is true even if ¬◇BIV. Realism entails more than this, as explained in the IEP article:

This general characterization of metaphysical realism is enough to provide a target for the Brains in a Vat argument. For there is a good argument to the effect that if metaphysical realism is true, then global skepticism is also true, that is, it is possible that all of our referential beliefs about the world are false. As Thomas Nagel puts it, “realism makes skepticism intelligible,” (1986, 73) because once we open the gap between truth and epistemology, we must countenance the possibility that all of our beliefs, no matter how well justified, nevertheless fail to accurately depict the world as it really is. [See Fallibilism.] Donald Davidson also emphasizes this aspect of metaphysical realism: “metaphysical realism is skepticism in one of its traditional garbs. It asks: why couldn’t all my beliefs hang together and yet be comprehensively false about the actual world?” (1986, 309)

So, again, R → ◇BIV, ¬◇BIV ⊢ ¬R.

◇Kp does entail p. — Banno

No it doesn't, just as ◇p does not entail p. You appear to have confused ¬p ∧ ◇Kp with ◇(¬p ∧ Kp), despite my suggestion not to.

Another, again separate, point is that if p ⊭ (q ∧ ¬Kq) then p ⊨ (p→(q→Kq)). If p doesn't entail that there is something we don't know, then it entails that we know everything. — Banno

I don't understand what your logic is here.

I am saying nothing more than that if a sentence like "it is raining" is true then it is possible to know that the sentence "it is raining" is true, but that the same reasoning does not apply to a sentence like "it is raining and nobody knows that it is raining". It very explicitly does not allow the substitution that is central to Fitch's paradox.

What you describe here is as compatible with realism as antirealism. — Banno

I addressed this in an earlier post:

But then maybe we need to distinguish between two types of realism; one that denies phenomenalism/idealism and one that denies the (restricted) knowability principle. Labels notwithstanding, Devitt's "realism" might be consistent with Dummett's "anti-realism". — Michael

Semantic realism claims that every meaningful declarative sentence is either true or false, which entails that either the counterfactual sentence "if Hitler hadn't killed himself then he would have been assassinated" is true or it is false. This is not compatible with the claim that if such a counterfactual is true then it is possible to know that it is true, because it is impossible to know whether or not such a counterfactual is true.

I've brought up counterfactuals several times now, but I don't recall you ever addressing them, so perhaps you can now. Are counterfactual propositions like the above truth-apt?

...realism holds that ...stuff... is independent of what we say about it; anti-realism, that it isn't. — Banno

There is a difference between p → ◇Kp (if something is true then it is possible for someone to know that it's true) and Bp → p (if someone believes that something is true then it's true). If you are suggesting that anti-realism is arguing the latter then you misunderstand anti-realism.

But merely permitting global scepticism is not ground for concluding that realism is false: A→(Bv~B)⊭~A — Banno

The argument is:

R → ◇BIV, ¬◇BIV ⊢ ¬R

Then you reject "p↔︎◇Kp where p is basic". — Banno

Well, ◇Kp doesn't entail p, and so ¬p ∧ ◇Kp is consistent, and not to be confused with ◇(¬p ∧ Kp).

But the anti-realist accepts p → ◇Kp where p is basic.

It says that if p doesn't entail that there is something we don't know, then we can know p. — Banno

That would be ∀p((p ⊭ ∃q(q ∧ ¬Kq)) → (p → ◊Kp)).

I am saying ∀p∀q((p ⊭ (q ∧ ¬Kq)) → (p → ◊Kp)).

As an explicit example of what I am trying to symbolise, if "it is raining" is true then it is possible to know that it is raining, but "it is raining and nobody knows that it is raining" can be true even though it is not possible to know both that it is raining and that nobody knows that it is raining.

If p doesn't entail that there is something we don't know, then it entails that we know everything. — Banno

I don't see how you get to that conclusion. My formulation does not allow for step 2 in Fitch's paradox:

Now consider the instance of KP substituting line 1 for the variable p in KP:

(2) (p ∧ ¬Kp) → ◊K(p ∧ ¬Kp)

But symbols aside:

If something exists then it is possible to know that it exists, and if it is doing something then it is possible to know that it is doing that thing, and if it is not doing something then it is possible to know that it is not doing that thing, and if it doesn't exist then it is possible to know that it doesn't exist – with the same reasoning applied to the past, the future, and counterfactuals.

Nothing here entails that if something exists and is doing something then we actually know it, so if you're concluding from the above that we know everything then you're addressing a misrepresentation.

Isn't this just saying that what we know must be consistent? — Banno

It's saying that if "p" does not entail "q is true and not known to be true" then if "p" is true then it is possible to know that "p" is true.

It also looks compatible with the SKP: p↔︎◇Kp — Banno

It's certainly not compatible with that.

SKP entails p ∧ ¬Kp ↔︎ ◇K(p ∧ ¬Kp).

My restricted knowability principle explicitly allows for p ∧ ¬Kp ∧ ¬◇K(p ∧ ¬Kp).

But antirealism in contrast does seem to commit to one or other non-binary theory of truth. — Banno

With respect to counterfactuals, sure. The anti-realist will say that "if Hitler hadn't killed himself then he would have been assassinated" is neither true nor false.

Whereas the realist would have to argue that either it is true or it is false, but then that opens up difficult questions about the reality of counterfactual truthmakers.

I don't see that it counts against realism that it might permit global skepticism. — Banno

If Putnam is correct then global skepticism is incoherent. Therefore if realism permits global skepticism then realism is false.

In what way does your concept of justice distinguish itself from your perception of pain? The sensation of pain or perception of magenta is just as much a construct of your brain as your concept of justice. — Christoffer

Well there's certainly a distinction between the concept of pain and the sensation of pain. They are both brain states but they're different kinds of brain states.

I don't think the concept of sight is of much comfort to a blind man.

Ideas exist in the physical world (ta-da). Justice is an idea. Ergo justice is real. — Pantagruel

I didn't say it isn't real. I said that I could see what someone would mean by saying that gravity is more real than justice.

There is the concept of gravity and there is gravity.
There is the concept of justice, but that's it.

With gravity there is a physical thing distinct from our brain states that "corresponds" to the concept, but with justice there isn't.

I distinguish sensations from concepts. Colour is like pain, not like justice.

If I were to represent your first argument symbolically, the first one would be:

P→Q
~P
Therefore Q. — NotAristotle

These are two different arguments:

P1. If I am a human woman then I am a human: P → Q
P2. I am a human woman: P
C1. Therefore, I am a human: Q

P1. If I am a human woman then I am a human: P → Q
P2. I am not a human woman: ¬P
C1. Therefore, I am a human: Q

The first is valid, P1 is true, P2 is false, and C1 is true
The second is invalid, P1 is true, P2 is true, and C1 is true

If the imaginary could be summed up as the result of a physical specific state of our brain and its present energy distribution, would that not mean it is also existing? — Christoffer

Certainly my concept of justice exists as a physical brain state, but when we talk about justice we're not talking about people's brain states.

Well, one definition of "real" is "existing or occurring in the physical world; not imaginary, fictitious, or theoretical; actual".

Justice, for example, isn't a physical thing – or at least not a physical thing in the sense that gravity is a physical thing.

Gravity
Kings
Justice

I could see what someone would mean by saying that gravity is "more real" than kings and that kings are "moral real" than justice.

There's an extensional component to "gravity" that "justice" doesn't have (unless Platonism is correct), and there's an intensional component to "kings" that "gravity" doesn't have.

If any premises are false, a valid argument will result in a conclusion that is necessarily false — NotAristotle

A valid argument with a false premise will result in a false conclusion — Leontiskos

Incorrect.

P1. If I am a human woman then I am a human
P2. I am a human woman
C1. Therefore, I am a human

The argument is valid. It's modus ponens. P1 and C1 are true. But P2 is false.

Also:

P1. If I am a woman then I am English
P2. I am a woman
C1. Therefore, I am English

The argument is valid. It's modus ponens. C1 is true. But P1 and P2 are false.

But this will not work with medium size small goods - with cats in boxes. If the cat is in the next room, with the box, but unobserved, there is a place for saying that it is either in the box or it is not — Banno

And the antirealist will agree, because the antirealist denies the conclusion of Fitch's argument (either because they are intuitionists or because they only argue for a restricted knowability principle). The antirealist only claims that if the cat is in the box then it is possible to know that the cat is in the box, whereas the realist allows for the impossibility of knowing, e.g. they will claim that in at least one case the cat is in the box but either it is impossible in principle to look in the box and see the cat or looking in the box and seeing the cat does not justify the belief that the cat is in the box. This kind of scenario, according to someone like Dummett, is incoherent.

You seem to want to do more than to reject those things that it is logically impossible to know...? — Banno

I'm suggesting just the bare minimum to avoid Fitch's paradox:

∀p∀q((p ⊭ (q ∧ ¬Kq)) → (p → ◊Kp))

The only unknowable truths are "p is an unknown truth".

And are either TKP or DKP intuitive to you? — Banno

I think my version is TKP. His phrasing is just a little more general, claiming that if it is a contradiction to know some p then we cannot know p. I'm just not sure what other than "p is an unknown truth" this would include.

So to the first section, in which Devitt characterises realism as the view that physical entities exist independently of the mental. Devitt notes with considerable glee that there is nothing in this definition about truth. He goes on to point out that truth is independent of the evidence at hand. "Truth is one thing, our means of discovering it, another". Hence, according to Devitt, "no doctrine of truth is constitutive of realism". — Banno

Antirealism isn't simply phenomenalism or idealism; it can be consistent with physicalism (and property dualism).

I think the IEP article on brains in a vat provides a better account:

One proposal is to construe metaphysical realism as the position that there are no a priori epistemically derived constraints on reality (Gaifman, 1993).

...

One virtue of this construal is that it defines metaphysical realism at a sufficient level of generality to apply to all philosophers who currently espouse metaphysical realism.

...

For there is a good argument to the effect that if metaphysical realism is true, then global skepticism is also true, that is, it is possible that all of our referential beliefs about the world are false. As Thomas Nagel puts it, “realism makes skepticism intelligible,” (1986, 73) because once we open the gap between truth and epistemology, we must countenance the possibility that all of our beliefs, no matter how well justified, nevertheless fail to accurately depict the world as it really is. Donald Davidson also emphasizes this aspect of metaphysical realism: “metaphysical realism is skepticism in one of its traditional garbs. It asks: why couldn’t all my beliefs hang together and yet be comprehensively false about the actual world?” (1986, 309)

But then maybe we need to distinguish between two types of realism; one that denies phenomenalism/idealism and one that denies the (restricted) knowability principle. Labels notwithstanding, Devitt's "realism" might be consistent with Dummett's "anti-realism".

I'll pause there. I gather we agree at least that this is the account being scrutinised? — Banno

Yes. So the anti-realist responds by either noting that antirealism rejects classical logic or by accepting that the knowability principle as written is too broad, offering instead a restricted version such as (9) in my post above which does not allow for the substitution (p ∧ ¬Kp) → ◇K(p ∧ ¬Kp).

(9) is consistent with (1) and so does not entail (5), and is even consistent with (2). If (9) is still anti-realism then anti-realism is consistent with (1), (2), (3), and (4). Therefore realism must be saying more than just (1), (2), (3), or (4).

My suggestion is that realism is saying that there are unknowable Cartesian truths, where a Cartesian truth is a truth that it is not a contradiction to know, e.g. some instance of "the cat is in the box".

So the anti-realist is claiming that if something exists then it is possible to know that it exists, and that if it is doing something then it is possible to know that it is doing that thing, and that if it isn't doing something then it is possible to know that it isn't doing that thing, and that if something doesn't exist then it is possible to know that it doesn't exist. None of this entails that we actually know everything.

I think the distinction between realism and anti-realism is more apparent when we consider counterfactuals and predictions. The realist, in accepting the principle of bivalence, will claim that all such propositions are either true or false, whereas the anti-realist will claim that if it is impossible in principle to know that a counterfactual or prediction is true or false then it is neither true nor false.

There seems to be a lot of ambiguous phrasing in this discussion and so I want to try to be as precise as possible:

1. For some p, p is true and unknown
∃p(p ∧ ¬Kp)

2. For some p, p is true and unknowable
∃p(p ∧ ¬◇Kp)

3. It is possible that for some p, p is true and unknown
◇∃p(p ∧ ¬Kp)

4. It is possible that for some p, p is true and unknowable
◇∃p(p ∧ ¬◇Kp)

5. For all p, if p is true then p is known
∀p(p → Kp)

6. For all p, if p is true then p is knowable
∀p(p → ◇Kp)

The realist accepts (1), (2), (3), and (4) and rejects (5) and (6).

The anti-realist accepts (1), (3) and (6) and rejects (2) and (5). They probably also reject (4), although strictly speaking (4) is consistent with (6).

The problematic proposition is:

7. For all p, it is possible that p is true and unknowable:
∀p(◇(p ∧ ¬◇Kp))

This entails radical scepticism:

8. For all p, if p is true then p is not known:
∀p(p → ¬Kp)

If the realist rejects (8) then they must reject (7). Note specifically the differences between (3), (4), and (7). (7) entails (3) and (4) but neither (3) nor (4) entail (7).

But we must ask whether or not (6) really is necessary for anti-realism, and so whether or not (2) really is sufficient for realism. As the SEP article mentions, some anti-realists offer a restricted knowability principle, perhaps such as the one I offered earlier:

9. For all p and all q, if p being true does not entail that q is an unknown truth then if p is true then p is knowable
∀p∀q((p ⊭ (q ∧ ¬Kq)) → (p → ◊Kp))

This is consistent with (2), avoiding Fitch's paradox even in classical logic, but is still sufficiently anti-realist, e.g. it still asserts that if some object exists then it is possible to know that it exists. It simply acknowledges that knowing that something is an unknown truth is a contradiction.

Given this, realism must be more than just (1), (2), (3), or (4). But if it isn't (7) then what is it? Perhaps the claim that there is at least one unknowable Cartesian truth (using Tennant's terminology), e.g. that there is at least one unknowably true "the object exists"?

And note the difference between "there is at least one unknowable Cartesian truth" and "it is possible that at least one Cartesian truth is not known". These are (2) and (3) respectively (restricted to Cartesian truths). Anti-realism is consistent with (3).

∀p(◊(p ∧ ¬◊Kp)) says "For all truths p, it is possible that p is true and it not be possible to know p"

I think that should be "For all truths p, it is possible that p is true and yet p is not known". That would be ∀p(◊(p ∧ ¬Kp)). — Banno

There are two different claims:

1. It is possible for the truth to be unknowable
2. It is possible for the truth to be unknown

These are represented as:

1. ∀p(◊(p ∧ ¬◊Kp))
2. ∀p(◊(p ∧ ¬Kp))

Certainly (2) is true, but at least according to that SEP article realists believe that (1) is also true, and as mentioned above, (1) entails that nothing is known.

Our concern is whether or not truths are knowable not just whether or not truths are known.

Linda McMahon for Secretary of Education and Dr Oz for Centers for Medicare and Medicaid Services. :chin:

I address that here.

If "for all p, it is possible that p is unknowably true" is true then "for all p, if p is true then p is necessarily not known" is true.

I think something like "for all p, it is possible that p is unknowable".

So take any proposition at random, e.g. that there is a suitcase under my bed. Is it possible that this is unknowable? Given that the realist argues for "mind-independent" truths, or as Gaifman describes it "that there are no a priori epistemically derived constraints on reality", it would seem that the realist must answer in the affirmative. Which, under S5, entails that it is necessarily unknown.

Some more general musings.

From here, we have these sets of propositions:

1. "the cat is in the box" is true and justified (is known)
2. "the cat is in the box" is false and justified (is not known)
3. "the cat is in the box" is true and unjustified (is not known)
4. "the cat is in the box" is false and unjustified (is not known)

5. "the cat is in the box" is true and I have looked in the box and seen the cat
6. "the cat is in the box" is false and I have looked in the box and seen the cat
7. "the cat is in the box" is true and either I have not looked in the box or I have not seen the cat
8. "the cat is in the box" is false and either I have not looked in the box or I have not seen the cat

There is perhaps a reasonable argument that if (6) is possibly true then (5) does not entail (1); that if it is possible that I look in the box and see the cat even if the cat is not in the box then looking in the box and seeing the cat does not justify the belief that the cat is in the box.

This would seem to be skepticsm.

One response is to deny the possibility of (6), and so also (2), leaving us with:

1. "the cat is in the box" is true and justified (is known)
3. "the cat is in the box" is true and unjustified (is not known)
4. "the cat is in the box" is false and unjustified (is not known)

Which can be simplified to:

a. "the cat is in the box" is justified (is known)
b. "the cat is in the box" is true and unjustified (is not known)
c. "the cat is in the box" is false and unjustified (is not known)

Jp ⊨ Kp ⊨ p

If a proposition is justified then it is true.

This would seem to be a type of antirealism.

That applies to TKP rather than KP. I don't agree that we only know things that are not contradictory - cartesian truths. So while any particular truth might not have been known, it does not follow that every given truth is unknown. We do know things. That is, the "p" in your logic is all truths when it should be a particular truth. — Banno

So we have two propositions:

1. The realist believes that it is possible for truth to be unknowable in principle.
2. The realist believes that truth is unknowable in principle.

The article asserted (1), not (2).

The problem for the realist, however, is that (under S5), (1) entails (2):

∀p(◊(p ∧ ¬◊Kp)) ⊢ ∀p(p → □¬Kp))

Hence my earlier claim that one of these is true:

1. Realism is incorrect
2. S5 is incorrect
3. Nothing is known

Fitch’s Paradox of Knowability:

He also points out that TKP, rather than the unrestricted KP, serves as the more interesting point of contention between the semantic realist and anti-realist. The realist believes that it is possible for truth to be unknowable in principle. Fitch’s reasoning, at best, shows us that there is structural unknowability, that is, unknowability that is a function of logical considerations alone. But is there a more substantial kind of unknowability, for instance, unknowability that is a function of the recognition-transcendence of the non-logical subject-matter? A realist decrying the ad hoc nature of TKP (or DKP) fails to engage the knowability theorist at the heart of the realism debate.

You seem to think that a realist will say that nothing is knowable. — Banno

That follows from the claim, quoted from the SEP article, that "the realist believes that it is possible for truth to be unknowable in principle".

If it is possible that a true sentence is unknowable then it is possibly not possible that a true sentence is known, and if it is possibly not possible that a true sentence is known then it is necessarily not possible that a true sentence is known.

◇¬◇p→□¬◇p

What?!? — Banno

1. "the cat is in the box" is true and I have looked in the box and seen the cat
2. "the cat is in the box" is true and justified

If "the cat is in the box" is true then is it possible to look in the box and see the cat?
Does (1) entail (2)?

If "yes" to both then if "the cat is in the box" is true then it is knowable.

If "the cat is in the box" being true is not knowable then either (1) does not entail (2) or it is not possible to look in the box and see the cat.

Do you disagree with any of this?

If the existence of objects is mind-independent then the truth of “the object exists” is mind-independent such that it could be true even if it is not possible, in principle, to know that it’s true.

There’s a reason that Dummett, the man who coined the term “antirealism”, framed the dispute between realism and antirealism as a dispute about the logic of truth.

Read further in the article you posted, under “6. Views Opposing the Independence Dimension (I): Semantic Realism”.

I'm going to try to summarise the reasoning. I'm taking it for granted that knowledge is justified true belief.

Given that the proposition "the cat is in the box" is believed to be true, there are prima facie four possible scenarios:

1. "the cat is in the box" is true and justified (is known)
2. "the cat is in the box" is false and justified (is not known)
3. "the cat is in the box" is true and unjustified (is not known)
4. "the cat is in the box" is false and unjustified (is not known)

In more specific terms:

5. "the cat is in the box" is true and I have looked in the box and seen the cat
6. "the cat is in the box" is false and I have looked in the box and seen the cat
7. "the cat is in the box" is true and either I have not looked in the box or I have not seen the cat
8. "the cat is in the box" is false and either I have not looked in the box or I have not seen the cat

The anti-realist claims that (5) entails (1) and that if "the cat is in the box" is true then it is possible in principle to look in the box and see the cat. If both of these claims are true then if "the cat is in the box" is true then it is knowable.

Whereas, as explained here, "the realist believes that it is possible for truth to be unknowable in principle."

Which means that the realist believes either that (5) does not entail (1) or that it if "the cat is in the box" is true then it is possibly not possible to look in the box and see the cat. Either entails that if "the cat is in the box" is true then it is unknowable¹.

¹ _{In S5, ◇¬◇p ⊢ □¬p. Technically the realist could reject S5, but as mentioned here, "this result suggests that S5 is the correct way to formulate a logic of necessity."}

Addendum: In fact, ◇¬◇p ⊢ □¬p can be applied to the very claim that "it is possible for truth to be unknowable in principle": if it is possibly not possible to know the truth then the truth is necessarily unknown.

Therefore, one of these is true:

1. Realism is incorrect
2. S5 is incorrect
3. Nothing can be known

It is true that there is gold in Boorara. If all life disappeared from the universe, but everything else is undisturbed, then it would still be true that there is gold in Boorara. — Banno

Let's take mathematical antirealism; we might say that a mathematical proposition is true if it is provable from the axioms. The mathematical antirealist doesn't then claim that if everyone were to die then mathematical propositions are no longer true; they continue to be true because they continue to be provable – there's just nobody around to prove them anymore, which is irrelevant.

Sure, something might be (as yet) unjustified and yet could be justified. In which case, since it could be justified, there is something which counts as it's justification. — Banno

What does it mean that something counts as its justification? Are you just repeating the claim "p can be justified"? What is the difference between (1) and (3)?

It woudl help considerably if you explained what you think a justification might be. I've already pointed out that mere logical entailment will not do. — Banno

It's whatever distinguishes knowledge from a mere true belief.

As a specific example, if "the cat is in the box" is true then perhaps the strongest justification is looking in the box and seeing the cat. That's an ordinary reason that we can be said to know that the cat is in the box.

Given that looking in the box and seeing the cat is always possible in principle, every case of "the cat is in the box" being true is justifiable, even if it hasn't yet been justified (i.e. we haven't yet looked in the box) – and even if it never is justified (i.e. we never look in the box).

So, at the very least, we should be antirealists about cats in boxes.

You want (1) not to entail (3). — Banno

I don't even know what (3) is. You won't explain it.

Again, I suspect you are equivocating. First you treat (2) and (3) as meaning different things, allowing you to say that (3) follows from (1) without saying that (2) follows from (1), and then you treat (2) and (3) as meaning the same thing, allowing you to say that if (2) is false then (3) is false.

So spell it out for me. What does (3) mean? How does it differ from (1) and (2)?

As it stands, anti-realism simply says that (1) is always true and (2) is sometimes false. And that's it. There is no additional proposition (3).

(1) entails (3). (2) entails (3). — Banno

So you have:

P1. If (1) then (3)
P2. If (2) then (3)

And then you seem to go:

C1. If not (2) then not (3).

That's denying the antecedent.

It would still really help if you explain what (3) means, and how it differs from (1) and (2).

This is your game. you get to decide, I supose. — Banno

You're the one who has introduced new grammar, so you need to explain it.

1. p can be justified
2. p is justified
3. p has a justification

I can't help but think that you're equivocating. You say that (1) entails (3), say that (2) is false, somehow use that to conclude that (3) is false, and so use that to conclude that (1) is false.

Sure. But "can be justified" entails "has a justification". — Banno

What is the difference between "is justified" and "has a justification"?

Only if you do not wish to allow for justifications in other possible worlds. — Banno

What? It doesn't follow because it doesn't follow, just as the spouse example doesn't follow.

Your other analogs do not work. — Banno

They work perfectly. They show that your re-phrasing of the claim has changed the meaning of the claim.

Do you really want to say that if a proposition is true than in some possible world there is a justification? Fine, then for you every truth has a justification. — Banno

That simply does not follow.

If some entity is a person then in some possible world it has a spouse. Therefore, every person has a spouse?

No, obviously not.

If every truth is justifiable, then for every truth there is some justification. — Banno

Just no.
"can be justified" does not entail "is justified".
"can be killed" does not entail "is killed".
"can be broken" does not entail "is broken".

It's honestly crazy that I have to explain this to you.

The point of that was to show that there is a meaningful difference between these two propositions:

1. If A is B then it can C
2. A can be B only if it has C

Banno is repeatedly misinterpreting/misrepresenting (1) as (2).

Sure you do. If you want to deny A→B then you must give an example of A^~B. — Leontiskos

Firstly, I don't. One approach is to show that A→B is a contradiction or is in some other sense incoherent. Antirealists often do this by addressing the meaning of the word "true" and explain that this meaning is inconsistent with unknowability.

Secondly, it is the realist who denies p → ◇Kp, and so if you follow your own reasoning you must provide an example of an unknowable truth.

Were Michael to disagree with this, he would have to show us a justifiable truth with no justifcation. — Leontiskos

No I don't. Just as the realist doesn't have to show us an unknowable truth.

Another example:

1. If the vase is fragile then it can break
2. The vase can be fragile only if it has a break

These do not mean the same thing. (1) is true and (2) is false.

If, for antirealists, as you say, all truths are believable and justifiable, you can drop the modality. p→Jp — Banno

No we can't. Dropping modality changes meaning.

These mean different things:

1. All truths are believed and justified
2. All truths are believable and justifiable

↪Michael It says that if something is mortal, then there is an something which is the death of that thing. Pretty plain. — Banno

This still doesn't explain what that means.

In ordinary English we say that if something is mortal then it can die; we don't say that if something is mortal then something it its death. I understand the former, not the latter.